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arXiv · 1611.00525

Rings over which every matrix is the sum of two idempotents and a nilpotent

H. Chen·M. Sheibani
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Abstract

A ring $R$ is (strongly) 2-nil-clean if every element in $R$ is the sum of two idempotents and a nilpotent (that commute). Fundamental properties of such rings are discussed. Let $R$ be a 2-primal ring. If $R$ is strongly 2-nil-clean, we show that $M_n(R)$ is 2-nil-clean for all $n\in {\Bbb N}$. We also prove that the matrix ring is 2-nil-clean for a strongly 2-nil-clean ring of bounded index. These provide many classes of rings over which every matrix is the sum of two idempotents and a nilpotent.

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H. Chen, M. Sheibani. 2016-11-02. Rings over which every matrix is the sum of two idempotents and a nilpotent. https://arxiv.org/abs/1611.00525

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